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A304036 Number of partitions of n into at most 2 copies of 1!, 3 copies of 2!, 4 copies of 3!, ... . 4

%I

%S 1,1,2,1,2,1,3,2,3,1,2,1,3,2,3,1,2,1,3,2,3,1,2,1,4,3,5,2,4,2,5,3,4,1,

%T 2,1,3,2,3,1,2,1,3,2,3,1,2,1,4,3,5,2,4,2,5,3,4,1,2,1,3,2,3,1,2,1,3,2,

%U 3,1,2,1,4,3,5,2,4,2,5,3,4,1,2,1,3,2,3,1,2

%N Number of partitions of n into at most 2 copies of 1!, 3 copies of 2!, 4 copies of 3!, ... .

%H Seiichi Manyama, <a href="/A304036/b304036.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Factoradic">Factorial number system</a>

%F G.f.: Product_{j>=1} Sum_{k=0..j+1} x^(k*j!) = Product_{j>=1} (1-x^((j+1)!+j!))/(1-x^(j!)).

%e a(6) = 3 because we have [6], [2,2,2] and [2,2,1,1].

%Y Cf. A001048, A064986, A303939, A304039.

%K nonn,look

%O 0,3

%A _Seiichi Manyama_, May 05 2018

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Last modified August 4 16:34 EDT 2020. Contains 336202 sequences. (Running on oeis4.)